Future Computing Needs for Reaction Theory

1. Future Computing Needsfor Reaction Theory Ian Thompson Nuclear Theory and Modeling Group, Lawrence Livermore National Laboratory This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and under SciDAC Contract DE-FC02-07ER41457 UCRL-PRES-235658 DoE review

2. (n+AXi) at energy Eprojectile Computational Workflow Eprojectile (UNEDF work) Target A = (N,Z) Ground state Excited states Continuum states TransitionDensities(r) Structure ModelMethods: HF, DFT, RPA, CI, CC, … Transitions Code UNEDF: VNN, VNNN…  Folding Code Veff for scattering Transition Potentials V(r) (Later: density-dependent & non-local) (other work) Deliverables Inelastic production Compound production Coupled ChannelsCode: FRESCO Partial Fusion Theory Hauser-Feshbach decay chains Residues (N’,Z’) Delayed emissions Compound emission Elastic S-matrix elements Voptical Preequilibrium emission Prompt particle emissions Fit Optical Potential Code: IMAGO Global optical potentials KEY: Code Modules UNEDF Ab-initio Input User Inputs/Outputs Exchanged Data Future research Reaction work here

3. Coupled Channels Sets • Coupled Channels Set • For each total spin J and parity  • For each target spin state I • For partial wave combination | (ls)j, I, J > • Solve coupled second-order differential equations • Each Jset is independent  parallel computations • No exchange: local couplings (so far) • With exchange and/or transfers: nonlocal couplings (iteration, or basis expansion) DoE review

4. Complexity Estimates • RPA 90Zr states up to 10, 20, 30 MeV • Core states: # 19, 109, 279 • Partial wave sets: # 97, 522, 1281 • Local couplings: • Do the 15 Jsets in parallel - 1 cpu-hour calculation. • Spreading of RPA states will be tested: • Estimate: 3000 core states, 50 000 partial waves • Scaling as N, so now ~ 60 000 hours. DoE review

5. CS ideas for improvements • Coupling matrices take up the space: • N*N full matrices for each radius! • Need CS for data generation & flow on multi-threaded nodes • Basis expansion methods, for non-local couplings • R-matrix methods have been tested (M functions/channel) • NM-square square matrix to solve: • Linear equations for single energy, otherwise full diagonalisation needed • Conjugate-gradient methods usable for single energy (in atomic scattering) • Replacing N coupled 2nd-order equations by 2N-parameter non-linear search optimisation (suggested by CS at Livermore) • Derivatives from reverse-direction adjoint solutions • Need best quadratic search methods • Scaling properties N may be different. DoE review